Question: Simplify the expression. $(2y^{4}-5y^{2}-7y)(3y^{4}+4y^{3})$
Solution: First use the distributive property. $ 2 y^4 (3 y^4) + 2 y^4 (4 y^3) - 5 y^2 (3 y^4) - 5 y^2 (4 y^3) - 7 y (3 y^4) - 7 y (4 y^3) $ Simplify. $ 6y^{8} + 8y^{7} - 15y^{6} - 20y^{5} - 21y^{5} - 28y^{4} $ $6y^{8}+8y^{7}-15y^{6}-41y^{5}-28y^{4}$ Identify like terms. $ { 6y^{8}} {+ 8y^{7}} {- 15y^{6}} {- 20y^{5}} {- 21y^{5}} {- 28y^{4}} $ Add the coefficients. $ { 6y^{8}} {+ 8y^{7}} { -15y^{6}} { -41y^{5}} { -28y^{4}} $